LPP Questions

Maximize $z=4x_1+3x_2$ subject to constraints:$2x_1+x_2\le 1000$$x_1+x_2\le 800$$x_1\le 400$$x_2\le 700$$x_1,x_2\ge 0$ Find the optimum units of $x_1$ and $x_2$ to be used.

Consider the Linear Programming problem:Maximize: $7X_1+6X_2+4X_3$ subject to:$X_1+X_2+X_3\le 5$$2X_1+X_2+3X_3\le 10$$X_1,X_2,X_3\ge 0$ The number of basic solutions is:

Maximize $z=5x_1+3x_2$ subject to the following constraints:$x_1+x_2\ge 3$$x_1-x_2\le 2$ and the solution is in the first quadrant ($x_1,x_2\ge 0$). What can be said about the solution of this LPP?

The minimum value of $3x+5y$ such that:$3x+5y\le 15$$4x+9y\le 18$$13x+2y\le 2$$x\ge 0,y\ge 0$ is:

For the linear programming problem:$\text{Maximize }Z=3X_1+2X_2$ Subject to:$-2X_1+3X_2\le 9$$X_1-5X_2\ge -20$$X_1,X_2\ge 0$ The above problem has:

A manufacturer produces two types of products, 1 and 2, at production levels of $x_1$ and $x_2$ respectively. The profit is $2x_1+5x_2$. Constraints are $x_1+3x_2\le 40$, $x_1+x_2\le 10$, $x_1\ge 0,x_2\ge 0$. The maximum profit is:

The minimum value of $z=5x-7y$, subject to the constraints $x+y\le 7$, $2x-3y+6\ge 0$, $x\ge 0,y\ge 0$, is: